Question

The number of silicon atoms per m³ is 5 × 10²⁸. This is doped simultaneously with 5 × 10²² atoms per m³ of Arsenic and 5 × 10²⁰ per m³ atoms of Indium. Calculate the number of electrons and holes. Given that n_i= 1.5 × 10¹⁶ m⁻³. Is the material n-type or p-type?

Answer 1

Number of silicon atoms, N = 5 × 10²⁸ atoms/m³

Number of arsenic atoms, n_As = 5 × 10²² atoms/m³

Number of indium atoms, n_In = 5 × 10²⁰ atoms/m³

Number of thermally-generated electrons, n_i = 1.5 × 10¹⁶ electrons/m³

Number of electrons, n_e = 5 × 10²² − 1.5 × 10¹⁶ ≈ 4.99 × 10²²

Number of holes = n_h

In thermal equilibrium, the concentrations of electrons and holes in a semiconductor are related as:

n_en_h = n_i²

`therefore "n"_"h" = ("n"_"i"^2)/"n"_"e"`

`= (1.5 xx 10^16)^2/(4.99 xx 10^22) ~~ 4.51 xx 10^9`

Therefore, the number of electrons is approximately 4.99 × 1022 and the number of holes is about 4.51 × 109. Since the number of electrons is more than the number of holes, the material is an n-type semiconductor.